International Journal of Computer Networks & Communications (IJCNC) Vol.9, No.5, September 2017 PERFORMANCE ANALYSIS OF CHANNEL CAPACITY AND THROUGHPUT OF LTE DOWNLINK SYSTEM P.Poornima 1, G. Laxminarayana 2 and D. Srinivas Rao 3 1Associate Professor, Dept. of ECE, Sphoorthy Engineering College, Hyderabad, India 2Professor, Dept. of ECE, Anurag College of Engineering, Hyderabad, India 3 Professor, Dept. of ECE, JNTUH CEH, Kukatpally, Hyderabad, India ABSTRACT In this paper, we analyzed a numerical evaluation of the performance of MIMO radio systems in the LTE network environment. Downlink physical layer of the OFDM-MIMO based radio interface is considered for system model and a theoretical analysis of the bit error rate of the two space-time codes (SFBC 2×1 and FSTD 4×2 codes are adopted by the LTE norm as a function of the signal to noise ratio. Analytical expressions are given for transmission over a Rayleigh channel without spatial correlation which is then compared with Monte-Carlo simulations. Further evaluated channel capacity and simulation results show throughput almost reaches to the capacity limit. KEYWORDS Channel Capacity, MIMO, OFDM, LTE Downlink, Spate time Block Coding and Throughput. 1. INTRODUCTION LTE is designed to meet carrier needs for high-speed data and media transport as well as high- capacity voice support well into the next decade. The LTE PHY employed some advanced technologies like Orthogonal Frequency Division Multiplexing (OFDM) and Multiple Input Multiple Output (MIMO) to provide downlink speed up to 100 Mbps [1-3]. The combination of OFDM and MIMO with spatial multiplexing (SM) scheme is viewed as a viable means to achieve high user information rates. In cellular networks, the same radio spectrum is reused in different cells, in order to improve the network capacity [5,6]]. Several authors have considered the effect of increasing the density of base stations in the network, and improvements in the network capacity with increasing base station density have been revealed [7]. For a MIMO LTE system, a significant spectral efficiency improvement of 17% over SIMO LTE for static scenarios is achieved though slightly over 29% performance drop occurs when a mobility of 29 mph is introduced [9,10,11]. Hence it is established that in deploying diversity techniques, spectral efficiency is not the target rather diversity gain is. In [11, 12], a performance of 2x2STBC and SM are evaluated using typical OFDM based system Receiver Transmitter Channel Coding Modulation Mapper S/P Converter IFFT P/S Converter Channel Decoding Modulation Damper P/S Converter IFFT S/P Converter Wireless Channel with AWGN throughput and BER as metrics of measurement. In [13, 14, 15] the performance of MIMO in LTE is viewed from the capacity perspective. DOI: 10.5121/ijcnc.2017.9505 55 International Journal of Computer Networks & Communications (IJCNC) Vol.9, No.5, September 2017 Despite of these advantages due to the combination of OFDM and MIMO in the physical layer, there are many problems that are to be answered to achieve data rate as per the standards. The established distribution of resources allows to utilize system capacity for the evaluation of performance [2, 3]. This paper analyses channel capacity for the MIMO-OFDM system using with spatial multiplexing and This paper is organized as In section II, channel capacity analysis of LTE system with spatial multiplexing and diversity techniques. Section III, A framework on channel capacity with space time coding scheme with SFBC and FSTD is presented. Throughput analysis for the various M- QM schemes under proposed space time coding is represented in Section IV .In Section V, we present numerical analysis and simulation results depicting the performance of the proposed system. Section VI, we conclude. 2. CHANNEL CAPACITY ANALYSIS FOR LTE SYSTEMS The channel capacity of SISO systems is described by the information theory based on the mathematical frame work introduced by Shannon [5]. In fact, it is the theory of information that communication systems have evolved to their present form. MIMO systems are no exception to this rule since Telstar [6, 7] has extended the work of Shannon to the case of multiple antennas and on OFDM case. As an application of the theory, we will consider first the channel capacity for the spatial multiplexing MIMO scheme followed by the channel capacity of the different diversity schemes. A. CHANNEL MODEL AND CHANNEL CAPACITY OF SPATIAL MULTIPLEXING SCHEME MIMO channel capacity for single carrier system and in Rayleigh channel considered in multi antenna systems. Where let us consider vector transmission model with Nt t transmits antennas and Nr receive antennas, then the received signal is expressed as ρ y= H + n (1) Nt In the above model, ρ is the average signal to noise ratio and y represents the received vector of size Nr ×1 and s represents the transmitted vector of size Nt×1. The MIMO channel is represented by the H matrix of size Nr × Nt , whereas the noise is represented by the vector n of size Nr×1. The mutual information between the transmitted signal and the received signal, I(s; y) when the channel matrix H is deterministic and is known to the receiver which is given as: ρ H Isy(;)logdet= I + HCH (/) bpsHz (2) 2 Nr s Nt Where Cs is the covariance matrix of transmitted signal vector s and I is the identity matrix with dimension Nr.ρ is the average signal to noise ratio. By definition, the channel capacity is the maximum of the mutual information where the maximization is taken over all possible covariance matrixes Cs and hence the deterministic MIMO channel capacity can be written as: As is the covariance matrix of transmitted signal vector s and I is the identity matrix with dimension Nr.ρ is the average signal to noise ratio. By definition, the channel capacity is the 56 International Journal of Computer Networks & Communications (IJCNC) Vol.9, No.5, September 2017 maximum of the mutual information where the maximization is taken over all possible covariance matrix Cs and hence the deterministic MIMO channel capacity can be written as: CH( )= max(;) Isy ( bpsHz / ) (3) p( s ) I ρ H C( H )= max log2 det + HCs H ( bps / Hz ) (4) tr C s = N t Nr N t For fading channel, the channel matrix H is a random matrix and hence the associated channel capacity is also a random variable. To deal with the random behavior of the channel of the channel, the average of the above equation over the distribution of H with the given name of erotic MIMO channel capacity can be defined as: I ρ H CE = E max log2 det + HCs H ( bps / Hz ) (5) tr C s= N t Nr N t T the above derivation of the erotic MIMO channel capacity does not provide information to choose the covariance matrix of s (Cs) to get the maximum mutual information. To be able to compute the maximization, it should be clarified if the transmitter, the receiver, or both have perfect knowledge of the channel state information (CSI).If the channel matrix H is known at the transmitter, the transmit covariance matrix ( Cs) can be chosen to maximize the channel capacity for a given realization of the channel. If the channel matrix H is, however, known at the receiver, the optimal signal covariance matrix has to be chosen according to: Cs = I (6) With such covariance matrix, the erotic MIMO channel capacity becomes]: I ρ H CE = Elog2 det + HCHs ( bpsHz / ) (7) Nr N t B. CHANNEL MODEL AND CHANNEL CAPACITY OF DIVERSITY SCHEMES The erotic channel capacity in (7) is valid for channel matrix where different signals are transmitted independently and hence cannot be applied directly to the space time block coding where the signals are transmitted form of spatial block codes. In fact, an STBC scheme with Nt transmit with Nt transmit antennas and Nr receive antennas is generally characterized by the transmission matrix which has the general form [9, 10]: g g... g 11 21 Nt1 g g... g G = 12 22Nt 2 (8) . ... g g... g 1T 2 T Nt T 57 International Journal of Computer Networks & Communications (IJCNC) Vol.9, No.5, September 2017 Where gig represents a linear combination of the signal constellation components and their from conjugates. The gig is the ith transmit antenna in the jth time slot for i = 1, ..., Nt represents the number of time slots used to transmit S symbols. For such STBC, the equivalent AWGN scaled channel is given by: 1ln 2 ynT= HxwF nT + nT (9) Rc Where, and is the S × 1 complex matrix after STBC decoding and S represents the number of transmitted symbols. And is the transmitted S ×1 complex vector with each entry having energy Es/Nt, Es is the maximum total transmitted energy on the Nt transmit antennas per symbol time, and wnT is complex Gaussian noise with zero mean and variance N0/2 in each dimension. 2 2 ∑N ∑ M th HF = i=1 j = 1 h ij is the squared Fresenius norm of H, hij is the channel gain from the i th transmit antenna to the j receive antenna. Rc is the code rate of the STBC and defined as S/T, where T is the number of time slots to transmit one block code. From the equivalent AWGN channel in (9), it is shown that the effective instantaneous SNR at the receiver denoted as γ is given as: Es 2 γ = H F (10) Nt Rc N o which means that the channel matrix is converted into a scalar channel and hence the ergodic capacity of the equivalent STBC channel in (9) is given by: CER=c log12 ( + γ ) ( bpsHz / ) (11) or equivalently, by inserting (10) into (11): Es 2 CER=c log1 + H (/) bpsHz (12) 2 ( Nt R c N o F ) If the probability density function of the instantaneous SNR p(γs) is known, the ergodic capacity of the equivalent STBC can be evaluated using the following integral equation for capacity evaluation: ∞ CR=c ∫ log2() 1 + γ p() γs d γ s ( bpsHz / ) (13) 0 3.